Internal problem ID [5571]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF VARIATION OF
PARAMETERS. Page 71
Problem number: 2(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\left (\cot ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+y(x)=cot(x)^2,y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+\cos \relax (x ) c_{1}-2-\cos \relax (x ) \ln \left (\frac {1-\cos \relax (x )}{\sin \relax (x )}\right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 34
DSolve[y''[x]+y[x]==Cot[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sin (x)+\cos (x) \left (-\log \left (\sin \left (\frac {x}{2}\right )\right )+\log \left (\cos \left (\frac {x}{2}\right )\right )+c_1\right )-2 \\ \end{align*}